Yes, it is right to say "...a friend of Susan's". You can also say "...a friend of Susan" but this is becoming increasingly unusual.

This is an example of how common use can sometimes go against a particular grammar pattern, creating a form which is logically 'incorrect'. The rules of language are ultimately descriptive, not prescriptive. In other words, grammar describes language as it is used, not as someone would like it to be used. When a form becomes standard use it is the correct form, even if it is odd, inconsistent with other forms or illogical.

We use the pronoun its in the same way we use hers or his, with the difference that we use its when we are describing something which is not a person. However, it is quite rare as in many contexts it can be ambiguous, and so we usually prefer to use the noun rather than this particular pronoun. We also tend to avoid the possessive pronoun its at the end of a sentence.

It is possible to come up with examples. Imagine you are looking at a friend's car. You might say My car's colour is ugly but its is quite nice.

Even this example is rather awkward in my view and 'this one's' would be preferable. It is grammatically correct to use its here, however.

Anybody please offer me their feedback on the correctness or wrongness of the following sentence:
" This is Samantha's new car which is bought by hers elder son Matthew , after his marriage"
please feel free to inform any kind of mistake in the above sentence, but i am specifically interested to know that "is it correct to use HERS ELDER SON MATTHEW instead of HER ELDER SON MATTHEW "